Tetras lay eggs. The male must be present at the time that the eggs come out of her for them to be fertilized. If a female is egg-laden and by herself, she usually re-absorbs the eggs but sometimes develops egg binding (infected eggs). She can't lay the eggs alone although sometimes they do seep out (mostly with goldfish). Those eggs would not be fertile or viable.
Tetras are not truly "pregnant" but egg-laden during which time they look slightly enlarged. If a fish is hugely fat, it probably has something else going on like an internal bacterial infection like dropsy or fish tuberculosis or perhaps a kidney malfunction. We all hope your tetra is indeed egg-laden instead. In that case, keep her with the other tetras with some soft plants around like java moss.
For more on separating and caring for fry, see
http://www.fishpondinfo.com/breed.htm